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What is resonance? Here's an explanation about the cause of vibration and countermeasures in mechanical design!
What are vibration and resonance?
How come a person's voice can breaks a glass⁉
Ms. Hama: Mr. Hashimoto! I saw that a glass was broken only by a person's voice in a TV show other day. It's amazing that voice could do such a thing! What's going on?
Mr. Hashimoto: I see. It was a phenomenon caused by "Resonance". "Resonance" is an important content to consider when designing machines. This time, let's learn about "vibration and resonance" in detail.
Sound and Vibration
Mr. Hashimoto: First, let's grasp the sound and vibration. The sound we are hearing is the vibration of the air. "Vibration" is generated by hitting or rubbing objects, which becomes "vibration of air", transmitted to the ear and heard as "sound". Vibration are not transmitted without air (gas), water (liquid), metal (solid), etc., so you can not hear sound in "vacuum".
There are three elements of sound. Pressure (volume), pitch (frequency), and tone (waveform). Here's a table summarizes the details of sound and vibration.
■ Types of sound and vibration
| Sound | Vibration | ||
|---|---|---|---|
| Volume | Pressure change amount of air Sound pressure: dB (decibel) | Amplitude Use displacements, velocities, and accelerations depending on the application. |
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Displacement: m |  |
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| Speed: m/sec |  |
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| ・Usual conversation: 40-60 dB ・In the train: 80 to 100 dB ・Airplane noise: 120 dB |
・Acceleration: m/sec2 |  |
|
| Frequency | Pitch (= pitch of sound) | Frequency of mechanical vibration |
|
 ・Human audible frequency 20 to 20 kHz ・Low frequency: Piano lowest sound 27.5Hz ・High frequency sound: Piano highest sound 4186Hz |
・Frequency analysis tells from which part of a product does the sound come from. ・Understand the cause of natural frequency and resonance |
||
| * "Frequency" is the number of waves repeated per second, and is used to represent sound, vibration, current, etc. Unit is Hz (Hertz) |  |
||
| waveform | Tone | Mechanical characteristic |
|
| The sound of "A (la)" of tuning forks and violins (440Hz). Tones are determined by the overlap of the integer multiple period from 440Hz. | ・Understand the torque and vibration characteristics of the engine ・The torque fluctuation due to the explosion at the piston shows the characteristics and abnormalities. |
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Ms.Hama: I see. There is a close relationship between sound and vibration.
Mr. Hashimoto: Next, here I made a graph comparing vibration and human sense.
Mr. Hashimoto: The graph shows the amplitude on the vertical axis and the frequency on the horizontal axis. The low frequencies are slow, so you can see them with your eyes. When it is over 5Hz, you can not see it, but you can feel that it vibrates when you touch it with your hand. Furthermore, when the frequency become higher, you can't feel it but hear as noise. The sensors of human eye, fingertips, and ears are truely well made, and you unconsciously feel the difference in vibration and frequency.
Why do vibration and resonance happen?
Types of vibration and its mechanism of occuring
Mr. Hashimoto: Next, I will explain the types of vibration and their mechanisms. There are three main types of vibration: free frequency, forced vibration, and self-excited vibration. In addition, it is classified into linear vibration, bending vibration, torsional vibration depending on the direction of vibration.
| Classification by vibration occuring mechanism | ||
|---|---|---|
| Free vibration | Forced vibration | Self-excitation vibration |
| A phenomenon that once external force applied, the vibration will continue after stopping external force apply. | A phenomenon that periodic external force occurs vibration. When the frequency of the external force changes, the numbers of the vibration also change. | A phenomenon that vibration occurred by non-vibration external force. Vibrates at its natural frequency. |
| [Specific examples] ・Natural frequency in the linear direction ・Natural frequency of torsion ・Natural frequency in the bending direction |
[Specific examples] ・Motor rotational fluctuations ・Unbalanced ・Engine rotation fluctuation |
[Specific examples] ・Play the violin by a bow ・Squeal of brakes ・Tacoma Bridge resonance in the Kalman vortex of the wind |
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Ms.Hama: Other than equipment and motors related to mechanical design, even in familiar things such as musical instruments or brakes are also related with vibration. By analyzing ""vibration"", we can discover the cause of machine trouble faster.
Natural frequency and resonance
Mr. Hashimoto: Everything have own unique frequencies, which are called "natural frequencies." It is said that the "natural frequency" of human is 2 to 5 Hz, and we feels uncomfortable under such frequency band. The seats of vehicles such as automobile is designed to be free from such frequency band. "Natural frequency" can be confirmed by measurement system or calculation formula. For example, in the case of an engine generator, it can be obtained by the following calculation formula.
■Simple calculation formula for torsional natural frequencies of engine generator systems
■What is resonance?
When vibration is applied at the same frequency as the natural frequency, vibration become much larger (tens of times) than the size of the added vibration. This resonance magnification varies greatly depending on the material. It is said that 50 to 80 times for metals and 5 to 10 times for rubber and resin.
Mr. Hashimoto: The performance of breaking a wine glass by voice which you talked about in the beginning is a prime example of this "resonance phenomenon". Vibrate the air with your voice, adjust the frequency by pitch, and add forced vibration to the wine glass. If the "forced frequency" and the "natural frequency" of the wine glass match, a vibration larger than the added ones occurs, and the wine glass breaks.
Ms.Hama: There is such a relationship between natural frequencies and resonance. When and how does "resonance" happen? I would like to know in detail, including specific examples.
When does resonance happen?
Various resonance phenomenon
1. Resonance between engine and generator
When the periodic engine torque fluctuation and the natural frequency of the engine generator match in a certain rotation speed range, a resonance happens and the rubber body of the coupling must be damaged. (deformation, melting)
Products used：Products used: Highly flexible elastic couplings (CENTAFLEX)
Mr. Hashimoto: In the case of engine generators, there are resonance points in the normal operating speed range as shown by the red line in the right figure. By using a rubber coupling with a soft torsional stiffness and moving this resonance point to the low-speed rotation range, it is possible to avoid resonance by passing through the resonance point at the start of the engine.
It is also important to work on resonance issues in the development of rocket engines. In some cases, the turbine blade that rotates ultra-high speed with the turbopump of the engine is damaged by metal fatigue due to resonance. It is on developping how to avoid and prevent resonance by Simulations and actual machine tests.
2.Resonance due to vibration of servo & stepper motor
The stepper is a motor that rotate step by step according to pulse rate and is adopted for small actuators. Smooth rotation control is performed by microsteps, etc. But in some cases a resonance occured in the rotation range where there are minute vibration and mechanical natural frequencies. In addition, the servo motor may also resonant with the pulsating torque of the motor and the motor frame. It is necessary to grasp and avoid what kind of resonance is in the normal operating speed range.
Mr. Hashimoto: It is important to grasp the natural frequency of the device, the step frequency of the control system, and the resonance rotation range, and to avoid (pass). In some cases, resonance points are avoided from the rotation range used by softening the torsional rigidity of the coupling（Rubber-based coupling, Resin-based coupling） or hardening the torsional rigidity (metal plate spring coupling).
3.Vibration conveyor using resonance
A device that conveys materials & parts using vibration. Since the vibration is resonated and the conveyor itself oscillate with the energy, the capacity of the drive motor could be small. In the long conveyor, pivot point (oscillating point by resonance) increases, and smooth conveyance is possible.
Mr. Hashimoto: Recently, vibration power generation equipment using vibration has been developping. It is possible to generate electricity by sound or stepping on a mat laid on the floor (sound power generation, floor power generation). Resonance and vibration have rather negative images that break things, generate noise, and are harmful. But by technologies that uses vibration power generation and resonance can turn it into useful energy. It can be expected to be used for energy saving and storage.
Ms.Hama: Awesome mechanisms! I want to learn about resonance and vibration further and use it in design and technological development!!
Mr. Hashimoto, Miki Pulley Co., Ltd
Joined Miki Pulley in 1972. Worked as a Product Manager in the Marketing and Technology divisions in positions both in Japan and overseas. He has also been involved with other organizations through joint research projects with universities and specialist bodies. He currently works as technical adviser and staff trainer.
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